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Department:

MATH

Course Number:

3670

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every Semester

Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.

MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses.

Course Text:

*Introduction to Probability and Statistics for Engineers and Scientists*, 5th edition, by Sheldon M. Ross

Topic Outline:

- Probabilities of Events:

Random experiments, events, sets, and probabilities

Probabilities for equally likely outcomes, elementary counting

Independent events

Conditional probability, Bayes theorem

Applications - Random Variables and Their Distributions:

Discrete random variables: Binomial, geometric, Poisson, multinomial

Continuous random variables: Exponential, normal, gamma, Weibull

Poisson process, waiting times

Applications - Expected Values and Functions of Random Variables:

Expectations and variances of standard random variables

Expectations of functions of random variables

Chi-square as the square of a normal, sums of independent random variables and reproductive properties of standard distributions

Central limit theorem

Applications - Descriptive Statistics:

Random samples: data collection and presentation

Sample statistics: mean, median, quantiles - Statistical Estimation:

Point estimates and their properties

Probability distributions for estimator, the t and F distributions

Confidence intervals - Hypothesis Testing:

Single sample tests, means, variances

Comparison of two populations, means and variances

Applications - Simple Linear Regression and Correlation:

Fitting a regression line

Inferences on the regression

Predictions for future responses

Correlation

Applications